Given:The given algebraic expression is $5(x-2y)^2+3(x-2y)$.To do:We have to factorize the expression $5(x-2y)^2+3(x-2y)$.Solution:Factorizing algebraic expressions:Factorizing an algebraic expression means writing the expression as a product of two or more factors. Factorization is the reverse of distribution. An algebraic expression is factored completely when it is written as a product of prime factors.Here, we can factorize the expression $5(x-2y)^2+3(x-2y)$ by taking out the common factors. The highest common factor of an algebraic expression is the highest factor that can be divided into each of the terms with no remainder.The terms in the given expression are $5(x-2y)^2$ and $3(x-2y)$.We can observe that $(x-2y)$ is common ... Read More

Given:The given algebraic expression is $9a(6a-5b)-12a^2(6a-5b)$.To do:We have to factorize the expression $9a(6a-5b)-12a^2(6a-5b)$.Solution:Factorizing algebraic expressions:Factorizing an algebraic expression implies writing the expression as a product of two or more factors. Factorization is the reverse of distribution. An algebraic expression is factored completely when it is written as a product of prime factors.Here, we can factorize the expression $9a(6a-5b)-12a^2(6a-5b)$ by taking out the common factors. The highest common factor(HCF) of an algebraic expression is the highest factor that can be divided into each of the terms with no remainder.The terms in the given expression are $9a(6a-5b)$ and $-12a^2(6a-5b)$.We can observe that $(6a-5b)$ is common ... Read More

Given:The given algebraic expression is $7a(2x-3)+3b(2x-3)$.To do:We have to factorize the expression $7a(2x-3)+3b(2x-3)$.Solution:Factorizing algebraic expressions:Factorizing an algebraic expression implies writing the expression as a product of two or more factors. Factorization is the reverse of distribution. An algebraic expression is factored completely when it is written as a product of prime factors.Here, we can factorize the expression $7a(2x-3)+3b(2x-3)$ by taking out the common factors. The highest common factor of an algebraic expression is the highest factor that can be divided into each of the terms with no remainder.The terms in the given expression are $7a(2x-3)$ and $3b(2x-3)$We can observe that $(2x-3)$ is common to ... Read More

Given:The given algebraic expression is $2r(y-x)+s(x-y)$.To do:We have to factorize the expression $2r(y-x)+s(x-y)$.Solution:Factorizing algebraic expressions:Factorizing an algebraic expression implies writing the expression as a product of two or more factors. Factorization is the reverse of distribution. An algebraic expression is factored completely when it is written as a product of prime factors.Here, we can factorize the expression $2r(y-x)+s(x-y)$ by taking out the common factors. The highest common factor(HCF) of an algebraic expression is the highest factor that can be divided into each of the terms with no remainder.We can write $2r(y-x)+s(x-y)$ as, $2r(y-x)+s(x-y)=2r[-(x-y)]+s(x-y)$$2r(y-x)+s(x-y)=-2r(x-y)+s(x-y)$The terms in the given expression are $-2r(x-y)$ and $s(x-y)$.We can observe that ... Read More

Given:The given algebraic expression is $6x(2x-y)+7y(2x-y)$.To do:We have to factorize the expression $6x(2x-y)+7y(2x-y)$.Solution:Factorizing algebraic expressions:Factorizing an algebraic expression implies writing the expression as a product of two or more factors. Factorization is the reverse of distribution. An algebraic expression is factored completely when it is written as a product of prime factors.Here, we can factorize the given expression by taking out the common factors. The highest common factor of an algebraic expression is the highest factor that can be divided into each of the terms with no remainder.The terms in the given expression are $6x(2x-y)$ and $7y(2x-y)$.We can observe that $(2x-y)$ is common ... Read More

Given:The given expression is $ax^2y+bxy^2+cxyz$.To do:We have to factorize the expression $ax^2y+bxy^2+cxyz$.Solution:GCF:A common factor of two or more numbers is a factor that is shared by the numbers. The greatest common factor (GCF) of those numbers is found by finding all common factors of the numbers and selecting the largest one.The terms in the given expression are $ax^2y, bxy^2$ and $cxyz$.The numerical coefficient of $ax^2y$ is $1$The numerical coefficient of $bxy^2$ is $1$The numerical coefficient of $cxyz$ is $1$This implies, GCF of $1, 1$ and $1$ is $1$The common variables in the given terms are $x$ and $y$.The power of $x$ in $ax^2y$ is $2$The ... Read More

Given:The given expression is $x^2yz+xy^2z+xyz^2$.To do:We have to factorize the expression $x^2yz+xy^2z+xyz^2$.Solution:HCF:A common factor of two or more numbers is a factor that is shared by the numbers. The highest common factor (HCF) of those numbers is found by finding all common factors of the numbers and selecting the largest one.The terms in the given expression are $x^2yz, xy^2z$ and $xyz^2$.The numerical coefficient of $x^2yz$ is $1$The numerical coefficient of $xy^2z$ is $1$The numerical coefficient of $xyz^2$ is $1$This implies, HCF of $1, 1$ and $1$ is $1$The common variables in the given terms are $x, y$ and $z$.The power of $x$ in $x^2yz$ is ... Read More

Given:The given expression is $-4a^2+4ab-4ca$.To do:We have to factorize the expression $-4a^2+4ab-4ca$.Solution:GCF:A common factor of two or more numbers is a factor that is shared by the numbers. The greatest common factor (GCF) of those numbers is found by finding all common factors of the numbers and selecting the largest one.The terms in the given expression are $-4a^2, 4ab$ and $-4ca$.The numerical coefficient of $-4a^2$ is $4$The numerical coefficient of $4ab$ is $4$The numerical coefficient of $-4ca$ is $4$This implies, GCF of $4, 4$ and $4$ is $4$The common variable in the given terms is $a$.The power of $a$ in $-4a^2$ is $2$The power of ... Read More

Given:The given expression is $16m-4m^2$.To do:We have to factorize the expression $16m-4m^2$.Solution:HCF:A common factor of two or more numbers is a factor that is shared by the numbers. The highest common factor (HCF) of those numbers is found by finding all common factors of the numbers and selecting the largest one.The terms in the given expression are $16m$ and $-4m^2$.The numerical coefficient of $16m$ is $16$The numerical coefficient of $-4m^2$ is $4$This implies, $16=2\times2\times2\times2$$4=2\times2$HCF of $16$ and $4$ is $2\times2=4$The common variable in the given terms is $m$.The power of $m$ in $16m$ is $1$The power of $m$ in $-4m^2$ is $2$The monomial of common ... Read More

Given:The given expression is $9x^2y+3axy$.To do:We have to factorize the expression $9x^2y+3axy$.Solution:GCF:A common factor of two or more numbers is a factor that is shared by the numbers. The greatest common factor (GCF) of those numbers is found by finding all common factors of the numbers and selecting the largest one.The terms in the given expression are $9x^2y$ and $3axy$.The numerical coefficient of $9x^2y$ is $9$The numerical coefficient of $3axy$ is $3$This implies, $9=3\times3$$3=3\times1$GCF of $9$ and $3$ is $3$The common variables in the given terms are $x$ and $y$.The power of $x$ in $9x^2y$ is $2$The power of $x$ in $3axy$ is $1$The power ... Read More